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    Area of Science:

    • Optics and Photonics
    • Cavity Physics
    • Mathematical Physics

    Background:

    • Multipass optical cavities, such as Herriott cells, are crucial for various laser and spectroscopy applications.
    • Understanding the stability and field propagation within these cavities is essential for optimizing their performance.
    • Existing analysis methods may not fully capture the behavior of complex re-entrant designs.

    Purpose of the Study:

    • To introduce a new analytical framework for multipass optical cavities using linear canonical transforms.
    • To investigate the properties of re-entrant Herriott cell designs and their output field characteristics.
    • To apply this analysis to predict the stability of cavities used in interferometric delay lines for temporal pulse addition.

    Main Methods:

    • Application of the linear canonical transform formalism to analyze optical cavity behavior.
    • Modeling of multipass optical cavities, specifically Herriott cells with re-entrant designs.
    • Stability analysis of cavities integrated into interferometric delay lines.

    Main Results:

    • Demonstration that re-entrant designs in Herriott cells reproduce the input field at the output.
    • Identification of useful symmetries inherent in these re-entrant cavity configurations.
    • Prediction of cavity stability crucial for applications like temporal pulse addition.

    Conclusions:

    • The linear canonical transform provides an effective method for analyzing multipass optical cavities.
    • Re-entrant Herriott cell designs offer advantageous field reproduction and symmetry properties.
    • This analytical approach enhances the design and stability prediction of optical cavities for advanced applications.